Shannon had $442 less than Fabian. Shannon spent ¹₅ of her money and Fabian spent ⁴₇ of his money. In the end, Fabian and Shannon had the same amount of money left. Find the amount of money Fabian had at first.

	Shannon	Fabian	Difference
Before	5x3 = 15 u	7x4 = 28 u	13 u
Change	- 1x3 = - 3 u	- 4x4 = - 16 u
After	4x3 = 12 u	3x4 = 12 u

Fraction of Shannon's money left
= 1 - ¹₅
= ⁴₅

Fraction of Fabian's money left
= 1 - ⁴₇
= ³₇

Fabian and Shannon had the same amount of money in the end. Make the numerators the same. LCM of 4 and 3 is 12.

⁴₅ of Shannon's money = ³₇ of Fabian's money
¹²₁₅ of Shannon's money = ¹²₂₈ of Fabian's money

Amount that Shannon had at first = 15 u
Amount that Fabian had at first = 28 u

Amount that Shannon had less than Fabian had at first
= 28 u - 15 u
= 13 u

13 u = 442

1 u = 442 ÷ 13 = 34

Amount that Fabian had at first
= 28 u
= 28 x 34
= $952

Answer(s): $952